The Practice of Statistics



Chapter 1: Exploring Data

Key Vocabulary:

▪ individual

▪ variable

▪ frequency table

▪ relative frequency table

▪ distribution

▪ pie chart

▪ bar graph

▪ two-way table

▪ marginal distributions

▪ conditional distributions

▪ side-by-side bar graph

▪ association

▪ dotplot

▪ stemplot

▪ histogram

▪ SOCS

▪ outlier

▪ symmetric

▪ Σ

▪ [pic]

▪ spread

▪ variability

▪ median

▪ quartiles

▪ Q1, Q3

▪ IQR

▪ five-number summary

▪ minimum

▪ maximum

▪ boxplot

▪ resistant

▪ standard deviation

▪ variance

[pic]

Data Analysis: Making Sense of Data (pp.2-6)

1. Individuals are…

2. A variable is …

3. When you first meet a new data set, ask yourself:

• Who…

• What…

• Why, When, Where and How…

4. Explain the difference between a categorical variable and a quantitative variable. Give an example of each.

5. Give an example of a categorical variable that has number values.

6. Define distribution:

7. What are the four steps to exploring data?

• Begin by….

• Study relationships…

• Start with a …

• Then add…

8. Answer the two questions for the Check Your Understanding on page 5:

9. Define inference.

1. Analyzing Categorical Data (pp.8-22)

1. A frequency table displays…

2. A relative frequency table displays…

3. What type of data are pie charts and bar graphs used for?

4. Categories in a bar graph are represented by ___________ and the bar heights give the category __________________.

5. What is a two-way table?

6. Define marginal distribution.

7. What are the two steps in examining a marginal distribution?

8. Answer the two questions for the Check Your Understanding on page 14.

9. What is a conditional distribution? Give an example demonstrating how to calculate one set of conditional distributions in a two-way table.

10. What is the purpose of using a segmented bar graph?

11. Answer question one for the Check Your Understanding on page 17.

12. Describe the four steps to organizing a statistical problem:

• State…

• Plan…

• Do…

• Conclude…

13. Explain what it meant by an association between two variables.

2. Analyzing Categorical Data (pp.27-42)

1. What is a dotplot? Draw an example.

2. When examining a distribution, you can describe the overall pattern by its

S_____ O_____ C_____ S_____

3. If a distribution is symmetric, what does it look like?

4. If a distribution is skewed to the right, what does it look like?

5. If a distribution is skewed to the left, what does it look like?

6. Describe and illustrate the following distributions:

a. Unimodal

b. Bimodal

c. Multimodal

7. Answer questions 1-4 for the Check Your Understanding on page 31.

8. How are a stemplot and a histogram similar?

9. When is it beneficial to split the stems on a stemplot?

10. When is it best to use a back-to-back stemplot?

11. List the three steps involved in making a histogram.

12. Why is it advantageous to use a relative frequency histogram instead of a frequency histogram?

13. Answer questions 2-4 for the Check Your Understanding on page 35.

3. Analyzing Categorical Data (pp.50-67)

1. What is the most common measure of center?

2. Explain how to calculate the mean, [pic].

3. What is the meaning of (?

4. Explain the difference between [pic] and (.

5. Define resistant measure.

6. Explain why the mean is not a resistant measure of center.

7. What is the median of a distribution? Explain how to find it.

8. Explain why the median is a resistant measure of center?

9. How does the shape of the distribution affect the mean and median?

10. What is the range?

11. Is the range a resistant measure of spread? Explain.

12. How do you find first quartile Q1 and third quartile Q3?

13. What is the Interquartile Range (IQR)?

14. Is the IQR and the quartiles a resistant measure of spread? Explain.

15. How is the IQR used to identify outliers?

16. What is the five-number summary of a distribution?

17. Explain how to use the five-number summary to make a boxplot.

18. What does the standard deviation measure? How do we calculate it?

19. What is the relationship between variance and standard deviation?

20. What are the properties of the standard deviation as explained on page 64?

21. How should one go about choosing measures of center and spread?

Chapter 2: Modeling Distributions of Data

[pic]

Key Vocabulary:

▪ percentiles

▪ cumulative relative frequency graphs

▪ z-scores

▪ transforming data

▪ density curves

▪ median of density curve

▪ transform data

▪ mean of density curve

▪ standard deviation of density curve

▪ Normal curves

▪ Normal distributions

▪ 68-95-99.7 rule

▪ [pic]

▪ standard Normal distribution

▪ standard Normal table

▪ Normal probability plot

▪ [pic] mu

▪ [pic] sigma

▪

2.1 Describing Location in a Distribution (pp.84-103)

1. A percentile is…

1. Is there a difference between the 80th percentile and the top 80%? Explain.

2. Is there a difference between the 80th percentile and the lower 80%? Explain.

3. Refer to the “Cumulative Relative Frequency Graphs” section on page 86 to answer the following questions:

a. Explain how to find the relative frequency column.

b. Explain how to find the cumulative frequency column.

c. Explain how to find the cumulative relative frequency column.

4. Explain how to make a cumulative relative frequency graph.

5. What can a cumulative relative frequency graph be used to describe?

6. Answer the four questions for the Check Your Understanding on page 89.

7. Explain how to standardize a variable.

8. What information does a z – score provide?

9. Explain how to calculate and interpret a z- score.

10. What is the purpose of standardizing a variable?

11. Explain the effects of adding or subtracting a constant from each observation when transforming data.

12. Explain the effects of multiplying or dividing by a constant from each observation when transforming data.

13. Summarize the four steps for exploring quantitative data as outlined on page 99.

14. What is a density curve?

15. What does the area under a density curve represent?

16. Where is the median of a density curve located?

17. Where is the mean of a density curve located?

18. Answer questions 1 and 2 for the Check Your Understanding on page 103.

2. Normal Distributions (pp.110-128)

1. How would you describe the shape of a Normal curve? Draw two examples.

2. Explain how the mean and the standard deviation are related to the Normal curve.

3. Define Normal distribution and Normal curve.

4. What is the abbreviation for a Normal distribution with a mean ( and a standard deviation (?

5. Explain the 68-95-99.7 Rule. When does this rule apply?

6. Answer questions 1-3 for the Check Your Understanding on page 114.

7. What is the standard Normal distribution?

8. What information does the standard Normal table give?

9. How do you use the standard Normal table (Table A) to find the area under the standard Normal curve to the left of a given z-value? Draw a sketch.

10. How do you use Table A to find the area under the standard Normal curve to the right of a given z-value? Draw a sketch.

11. How do you use Table A to find the area under the standard Normal curve between two given z-values? Draw a sketch.

12. Summarize the steps on how to solve problems involving Normal distributions as outlined on page 120.

13. When is it appropriate to use Table A “backwards”?

14. Describe two methods for assessing whether or not a distribution is approximately Normal.

15. What is a Normal probability plot?

16. How do you interpret a Normal probability plot?

17. When is it appropriate to use the NormalCDF and Inverse Normal functions on the calculator?

Chapter 3: Describing Relationships

3.1 Scatterplots and Correlation (pp.142-156)

1. Why do we study the relationship between two quantitative variables?

2. What is the difference between a response variable and the explanatory variable?

3. How are response and explanatory variables related to dependent and independent variables?

4. When is it appropriate to use a scatterplot to display data?

5. A scatterplot shows the relationship between…

6. Which variable always appears on the horizontal axis of a scatterplot?

7. When examining a scatterplot, you can describe the overall pattern by its:

D_____ O_____ F_____ S_____

8. Explain the difference between a positive association and a negative association.

9. What is correlation r?

10. Answer the five questions for the Check Your Understanding on page 149.

11. What does correlation measure?

12. Explain why two variables must both be quantitative in order to find the correlation between them.

13. What is true about the relationship between two variables if the r-value is:

a. Near 0?

b. Near 1?

c. Near -1?

d. Exactly 1?

e. Exactly -1?

14. Is correlation resistant to extreme observations? Explain.

15. What do you need to know in order to interpret correlation?

3.2 Least-Squares Regression (pp.164-188)

1. What is a regression line?

2. In what way is a regression line a mathematical model?

3. What is the general form of a regression equation? Define each variable in the equation.

4. What is the difference between y and [pic]?

5. What is extrapolation and why is this dangerous?

6. Answer the four questions for the Check Your Understanding on page 167.

7. What is a residual? How do you interpret a residual?

8. What is a least-squares regression line?

9. What is the formula for the equation of the least-squares regression line?

10. The least-squares regression line always passes through the point ...

11. What is a residual plot? Sketch a graph of a residual plot.

12. If a least-squares regression line fits the data well, what two characteristics should the residual plot exhibit?

13. What is the standard deviation of the residuals? How is it interpreted?

14. How is the coefficient of determination defined?

15. What is the formula for calculating the coefficient of determination?

16. If r2 = 0.95, what can be concluded about the relationship between x and y?

______% of the variation in (response variable) is accounted for by the regression line.

17. When reporting a regression, should r or r2 be used describe the success of the regression? Explain.

18. Identify the slope, the y intercept, s and r2 on the computer output.

[pic]

19. What are three limitations of correlation and regression?

20. What is an outlier?

21. What is an influential point?

22. Under what conditions does an outlier become an influential observation?

23. What is a lurking variable?

24. Why does association not imply causation?

Chapter 4: Designing Studies

Key Vocabulary:

▪ sample

▪ population

▪ sample survey

▪ voluntary response sample

▪ confounded

▪ design

▪ convenience sampling

▪ biased

▪ simple random sample

▪ table of random digits

▪ probability sample

▪ stratified random sample

▪ cluster sampling

▪ inference

▪ margin of error

▪ strata

▪ undercoverage

▪ nonresponse

▪ response bias

▪ sampling frame

▪ systematic random sample

▪ observational study

▪ experimental

▪ confounding

▪ lurking variable

▪ experimental units

▪ subjects

▪ random assignment

▪ treatment

▪ factor

▪ level

▪ placebo effect

▪ single blind experiment

▪ control group

▪ completely randomized experiment

▪ randomized block design

▪ matched pair design

▪ statistically significant

▪ replication

▪ hidden bias

▪ double-blind experiment

▪ block design

▪ data ethics

4.1 Sampling and Surveys (pp.206-224)

1. Explain the difference between a population and a sample.

2. What is involved in planning a sample survey?

3. Why might convenience sampling be unreliable?

4. What is a biased study?

5. Why are voluntary response samples unreliable?

6. Define simple random sample (SRS).

7. What two properties of a table of random digits make it a good choice for creating a simple random sample?

8. State the two steps in choosing an SRS:

9. What is the difference between sampling with replacement and sampling without replacement?

10. How can you account for this difference with and without replacement when using a table of random digits or other random number generator?

11. How do you select a stratified random sample?

12. What is cluster sampling?

13. What is inference?

14. What is a margin of error?

15. What is the benefit of a larger sample size?

16. A sampling frame is…

17. Give an example of undercoverage in a sample.

18. Give an example of nonresponse bias in a sample.

19. Give an example of response bias in a sample.

20. How can the wording of questions cause bias in a sample?

21. Answer the two questions for the Check Your Understanding on page 224.

4.2 Experiments (pp.231-251)

1. Explain the differences between observational study and experiment.

2. A lurking variable is…

3. What problems can lurking variables cause?

4. Confounding occurs when…

5. Answer the four questions for the Check Your Understanding on page 233.

6. Explain the difference between experimental units and subjects.

7. Define treatment.

8. By studying the TV Advertising example on page 235, identify the factors and levels in the experiment.

9. Explain why the example, Which Works Better: Online or In-Class SAT Preparation, is a bad experiment.

10. What is random assignment?

11. What is a comparative experimental design?

12. In a completely randomized design…

13. Does using chance to assign treatments in an experiment guarantee a completely randomized design? Explain.

14. What is the significance of using a control group?

15. The basic principles of statistical design experiments are:

16. Define control, random assignment and replication in experimental design.

17. Describe the placebo effect.

18. What are the differences between a double-blind and single-blind experiement?

19. Define statistically significant.

20. What is a block?

21. What is a randomized block design?

22. When does randomization take place in a block design, and how does this differ to a completely randomized design?

23. What is the goal of a matched pairs design?

24. When is it beneficial to use a blocked/paired design? How should we choose which variables to block for?

4.3 Using Studies Wisely (pp.261-267)

1. Name the two types of inferences that can be identified based on the design of a study.

2. Name the challenges of establishing causation.

3. What are the four criteria for establishing causation when we can’t do an experiment?

4. Briefly describe the basics of data ethics.

Chapter 5: Probability: What are the chances?

Key Vocabulary:

▪ law of large numbers

▪ probability

▪ simulation

▪ two -way table

▪ sample space

▪ S = {H, T}

▪ tree diagram

▪ probability model

▪ replacement

▪ event

▪ P(A)

▪ complement AC

▪ disjoint

▪ mutually exclusive event

▪ Venn diagram

▪ union (or)

▪ intersection (and)

▪ conditional probability

▪ independent events

▪ general multiplication rule

▪ general addition rule

▪ multiplication rule

5.1 Randomness, Probability, and Simulation (pp.282-292)

1. What is the law of large numbers?

2. The probability of any outcome…

3. How do you interpret a probability?

4. Answer the two questions for the Check Your Understanding on page 286.

5. What are the two myths about randomness? Explain.

6. Define simulation.

7. Name and describe the four steps in performing a simulation:

8. What are some common errors when using a table of random digits?

5.2 Probability Rules (pp.299-308)

1. In statistics, what is meant by the term sample space?

2. In statistics, what is meant the term probability model?

3. What is an event?

4. What is the P (A) if all outcomes in the sample space are equally likely?

5. Define the complement of an event. What is the complement rule?

6. Explain why the probability of any event is a number between 0 and 1.

7. What is the sum of the probabilities of all possible outcomes?

8. Describe the probability that an event does not occur?

9. When are two events considered disjoint or mutually exclusive?

10. What is the addition rule for mutually exclusive events?

11. What is the probability of two disjoint events?

12. Summarize the five basic probability rules as outlined on page 302.

13. Answer the three questions for Check Your Understanding on page 303.

14. When is a two-way table helpful?

15. In statistics, what is meant by the word “or”?

16. When can a Venn diagram be helpful?

17. What is the general addition rule for two events?

18. What happens if the general addition rule is used for two mutually exclusive events?

19. What does the union of two or more events mean? Illustrate on a Venn diagram.

20. What does the intersection of two or more events mean? Illustrate on a Venn diagram.

5.3 Conditional Probabilty and Independence (pp.312-327)

1. What is conditional probablity? What is the notation for conditional probabilty?

2. Answer the two questions for the Check Your Understanding on page 314.

3. What are independent events?

4. What is the notation used for independent events?

5. Answer the three questions for Check Your Understanding on page 317.

6. When is a tree diagram helpful?

7. State the general multiplication rule for any two events.

8. State the multiplication rule for independent events.

9. How is the general multiplication rule different than the multiplication rule for independent events?

10. Explain the difference between mutually exclusive and independent.

11. State the formula for calculating conditional probabilities.

12. How is the conditional probability formula related to the general multiplication rule?

Chapter 6: Random Variables

Key Vocabulary:

▪ random variable

▪ discrete random variable

▪ probability distribution

▪ mean of a random variable

▪ variance of a random variable

▪ probability density curve

▪ continuous random variable

▪ standard deviation

▪ binomial setting

▪ binomial random variable

▪ binomial distribution

▪ binomial coefficient

▪ binomial probability

▪ linear transformation

▪ normal approximation

▪ geometric setting

▪ geometric distribution

▪ geometric random variable

▪ Normal approximation

▪ geometric probability

▪ factorial

▪ expected value

▪ standard deviation

▪ [pic]

▪ [pic]

▪ uniform distribution

6.1 Discrete and Continuous Random Variables (pp.341-352)

1. What is a random variable?

2. Define probability distribution.

3. What is a discrete random variable?

4. What are the two requirements for the probability distributions of discrete random variables?

5. If X is a discrete random variable, what information does the probability distribution of X give?

6. In a probability histogram what does the height of each bar represent (assuming the width of each bar is the same)?

7. In a probability histogram, what is the sum of the height of each bar?

8. What is the mean [pic]of a discrete random variable X?

9. How do you calculate the mean of a discrete random variable?

10. Define expected value. What notation is used for expected value?

11. Does the expected value of a random variable have to equal one of the possible values of the random variable? Explain.

12. Explain how to calculate the variance and standard deviation of a discrete random variable.

13. Explain the meaning of the standard deviation of a random variable X.

14. What is a continuous random variable and how is it displayed?

15. If X is a continuous random variable, how is the probability distribution of X described?

16. What is the area under a probability density curve equal to?

17. What is the difference between a discrete random variable and a continuous random variable?

18. If X is a discrete random variable, do [pic] and [pic] have the same value? Explain.

19. If X is a continuous random variable, do [pic] and [pic] have the same value? Explain.

20. How is a Normal distribution related to probability distribution?

6.2 Transforming and Combining Random Variables

(pp.358-375)

1. What is the effect on a random variable of multiplying or dividing by a constant?

2. How does multiplying by a constant effect the variance?

3. What is the effect on a random variable of adding or subtracting by a constant?

4. Define linear transformation.

5. What are the effects of a linear transformation on the mean and standard deviation?

6. Define the mean of the sum of random variables.

7. What are independent random variables?

8. Define the variance of the sum of independent random variables. What types of variables does it apply to?

9. When can you add the variances of two random variables?

10. State the equation for the mean of the difference of random variables?

11. State the formula for the variance of the difference of random variables.

12. What happens if two independent Normal random variables are combined?

13. Suppose [pic] = 5 and [pic] = 10. According to the rules for means, what is [pic]?

14. Suppose [pic] = 2. According to the rules for means, what is [pic]?

15. Suppose [pic] = 2 and [pic] = 3 and X and Y are independent random variables. According to the rules for variances, what is [pic]? What is [pic]?

16. Suppose [pic] = 4. According to the rules for variances, what is [pic]? What is [pic]?

6.3 Binomial and Geometric Random Variables (pp.382-401)

1. What is a binomial setting?

2. Describe the conditions of a binomial setting.

3. What is a binomial random variable and what are its possible values?

4. Define the parameters of a binomial distribution.

5. Explain the meaning of the binomial coefficient and state the formula.

6. Explain how to calculate binomial probabilities.

7. What commands on the calculator are used to calculate binomial probabilities?

8. Explain how to calculate the mean and standard deviation of a binomial random variable.

9. When can the binomial distribution be used to sample without replacement? Explain why this is an issue.

10. What is a geometric setting?

11. Describe the conditions for a geometric setting.

12. What is a geometric random variable and what are its possible values?

13. Describe the parameters of a geometric distribution.

14. What is the formula for geometric probability?

15. How is the mean of a geometric random variable calculated?

Chapter 7: Sampling Distributions

Key Vocabulary:

▪ parameter

▪ statistic

▪ sampling variability

▪ sampling distribution

▪ population distribution

▪ biased estimator

▪ unbiased estimator

▪ bias

▪ variability

▪ variability of a statisic

▪ sample proportion

▪ mean and standard deviation of sampling distributions

▪ central limit theorem

7.1 What Is a Sampling Distribution? (pp.414-428)

1. Explain the difference between a parameter and a statistic?

2. What is sampling variability?

3. Explain the difference between [pic] and [pic], and between p and [pic]?

4. What is meant by the sampling distribution of a statistic?

5. What is population distribution?

6. What is the difference between the distribution of the population, the distribution of the sample, and the sampling distribution of a sample statistic?

7. What is sampling variability?

8. Explain the difference between [pic] and [pic], and between p and [pic]?

9. What is meant by the sampling distribution of a statistic?

10. What is population distribution?

11. What is the difference between the distribution of the population, the distribution of the sample, and the sampling distribution of a sample statistic?

12. When is a statistic considered an unbiased estimator?

13. What is biased estimator?

14. How is the size of a sample related to the spread of the sampling distribution?

15. The variability of a statistic is…

16. Explain the difference between bias and variability.

7.2 Sample Proportions (pp.432-438)

1. What is the purpose of the sample proportion?

2. In an SRS of size n, what is true about the sampling distribution of [pic] when the sample size n increases?

3. In an SRS of size n:

a. What is the mean of the sampling distribution of [pic]?

b. What is the standard deviation of the sampling distribution of [pic]?

4. What happens to the standard deviation of [pic] as the sample size n increases?

5. When does the formula [pic] apply to the standard deviation of [pic]?

6. When the sample size n is large, the sampling distribution of [pic] is approximately Normal. What test can you use to determine if the sample is large enough to assume that the sampling distribution is approximately normal?

7.3 Sample Means (pp.442-452)

1. What are the mean and standard deviation of the sampling distribution of the sample mean [pic]? Describe the conditions for these formulas.

2. Explain how the behavior of the sample mean and standard deviation are similar to the sample proportion.

3. The mean and standard deviation of a population are parameters.

What symbols are used to represent these parameters?

4. The mean and standard deviation of a sample are statistics.

What symbols are used to represent these statistics?

5. The shape of the distribution of the sample mean depends on …

6. Because averages are less variable than individual outcomes, what is true about the standard deviation of the sampling distribution of [pic]?

7. What symbols are used to represent the mean and standard deviation of the sampling distribution of [pic]?

8. What is the mean of the sampling distribution of [pic], if [pic] is the mean of an SRS of size n drawn from a large population with mean μ and standard deviation σ?

9. What is the standard deviation of the sampling distribution of [pic], if [pic] is the mean of an SRS of size n drawn from a large population with mean μ and standard deviation σ?

10. When should you use [pic] to calculate the standard deviation of [pic]?

11. What is the Central Limit Theorem?

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